A crucible is a vessel used for heating materials to extremely high temperatures. It is particularly used to heat precious metals, and the exterior has no problem holding the material while it heats. A crucible has also come to be known as a great test or trial in one's life.
In the play The Crucible, many of the characters struggle under the scrutiny of the court. In fact, they are taken and questioned from a variety of perspectives for what seems like an eternity. Mary Warren exemplifies this phenomenon. She wanted to tell the truth, but the more time she spent answering questions from Danforth, the more she continued to figuratively get burned. Once the fire got too hot for her, she turned on her original purpose for being there answering questions (to protect the Proctor family from the falsehood that the girls were beginning to produce about them). The Crucible explores the themes of guillt and innocence, and truth and lies. It seems that in each of these paradoxical pairs, one can be exchanged for the other in the extreme circumstance of being in the court, rather the figurative crucible.
I also think of the crucible as a hot seat. One of the major themes of The Crucible is the political questioning that was going on in Congress at the time of Miller's writing. It was as if there was a modern day witch hunt in the 50s looking for those friendly to communists.